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15.401 Recitation 15.401 Recitation: 3: Common Stocks

This document provides an overview of key concepts in valuing common stocks, including discounted cash flow (DCF) valuation and the Gordon Growth Model. It then presents three examples to illustrate how to apply these models to value stocks. The first example values Flancrest Enterprises stock using a DCF approach with changing dividend growth rates. The second values CompuGlobalHyperMegaNet stock for different return on equity assumptions. The third discusses why rapidly growing earnings does not necessarily imply a comparable increase in expected stock returns.

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31 views15 pages

15.401 Recitation 15.401 Recitation: 3: Common Stocks

This document provides an overview of key concepts in valuing common stocks, including discounted cash flow (DCF) valuation and the Gordon Growth Model. It then presents three examples to illustrate how to apply these models to value stocks. The first example values Flancrest Enterprises stock using a DCF approach with changing dividend growth rates. The second values CompuGlobalHyperMegaNet stock for different return on equity assumptions. The third discusses why rapidly growing earnings does not necessarily imply a comparable increase in expected stock returns.

Uploaded by

abdul5721
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 15

15.

401 Recitation

3: Common Stocks
Learning Objectives
 Review of Concepts
o Discounted cash flow (DCF)

o PVGO

 Examplles

o Flancrest Enterprises
o ComppuGlobalHypyperMeggaNet
o Globex Corporation

2010 / Yichuan Liu 2


Review: DCF
 The stock price today = sum of all expected future
dividends discounted at the appropriate risk‐
adjusted rate.
 Constant dividend:
D
P00 
r
 Growing dividend (r > g):
D1
P0 
rg

2010 / Yichuan Liu 3


Review: DCF
 Components of DCF:
o D: dividend forecast based on historical data and future

prediction
o r: th
the di
discountt ratte = rf (risk‐free
(i kf ratte d
due to time
ti vallue off
money) + π (risk premium due to risk of dividend stream).
o g: growth rate based on…
• return on equity (ROE): earnings / book value of equity
• plowback ratio (b): retained earnings / total earnings
• g = ROE x b.
b.
• Note: g must be the long‐run growth rate.

2010 / Yichuan Liu 4


Review: PVGO
 We can separate the value of a firm into its ongoing
ongoing

value and value of growth opportunities:


EPS1
P0  V0 
 PVGO   PVGO
r
 PVGO can be solved from the above equation,
where
h P0 is
i dderived
i d from
f DCF.
DCF
 Conversely, we can find the implied rate of return on
a stock given market data:
D 1 D0 1 g 
r g g
P0 P0
2010 / Yichuan Liu 5
Example 1: Flancrest Enterprises
 Flancrest Enterprises recently paid a dividend of $1
per share. Its dividend is expected to grow at 20%
for years 1‐5. Afterwards, the growth rate will slow
down to 5%. If the cost of capital for Flancrest
Enterprises is 15%, what is the price of its stock
t d ?
today?
D= 1.2 1.22 …… 1.25 1.25x1.05 1.25x1.052 … …
0 1 2 …… 5 6 7 … … periods
 What is the ex‐dividend price of the stock at time 1?
What is the rate of return of the stock in Year 1?
2010 / Yichuan Liu 6
Example 1: Flancrest Enterprises

 Time 0:
D= 1.2 1.22 …… 1.25 1.25x1.05 1.25x1.052 … …
0 1 2 …… 5 6 7 … … periods

 PV of Year 1‐5:
1.2

1.2 

1.2 
2
 5.6912
5

15 1.15
1.15
1 1 15
2
1.15
15
5

1.25 1.05 1
 PV of Year 6‐∞:   12.9899
0.15  0.05 1 15

1.15
5

 Price: 5.6912 12.9899  $18.68

2010 / Yichuan Liu 7


Example 1: Flancrest Enterprises
 Time 1:
D= 1.22 …… 1.25 1.25x1.05 1.25x1.052 … …
0 1 2 …… 5 6 7 … … periods

 PV of Year 2‐5: 1.222  1.223    1.225  5.3449


1.15 1.152 1.154
25 1
1.2 1.05
05 1
 PV of Year 6‐∞:   14.9384
0.15  0.05 1.154

 Price:
P i 3449 14
5.3449 9384  $20.28
14.9384 $20 28
 Return: $20.28  $1.2
1  15.00%
$18 68
$18.68
2010 / Yichuan Liu 8
Example 2: CompuGlobalHyperMegaNet

 CompuGlobalHyperMegaNet (CGHMN) has an EPS


EPS

of $2 last year. It has a payout ratio of 25% and ROE


of 10%. If investors expect a return of 10% from the
firm,
o What is CGHMN’s stock price?
o What is CGHMN
CGHMN’ss PVGO?
o What is CGHMN’s P/E ratio?
 How would the answers change if
o ROE = 12%?
o ROE = 9%

2010 / Yichuan Liu 9


Example 2: CompuGlobalHyperMegaNet
 (ROE = 10%)
o g  ROE  b  0.1 1 0.25  0.075

D1 D0  1 g  2  0.25 1 0.075


P0     $21.50
$21 50
rg rg 0.10  0.075
o EPS1 2 1
1.075
075
PVGO  P0   21.5   $0.00
r 0.10

o P0 21 5

21.5
PE 0    10
EPS1 2 1.075

2010 / Yichuan Liu 10


Example 2: CompuGlobalHyperMegaNet
 (ROE = 12%)
o g  ROE  b  0.12  1  0.25  0.09

D1 D0  1  g  2  0.25  1  0.09 


P0     $54.50
$54 50
rg rg 0.10  0.09
o EPS1 2 1
1.09
09
PVGO  P0   54.5   $32.70
r 0.10

o P0 54.50
54 50

PE 0    25
EPS1 2 1.09

2010 / Yichuan Liu 11


Example 2: CompuGlobalHyperMegaNet
 (ROE = 9%)
o g  ROE  b  0.09 1 0.25  0.0675

. 1 0.0675
2  0.25 . 7 


P0   $16.42
16 42
0.10  0.0675
o EPS1 2 1
1.0675
0675
PVGO  P0   16.42   $4.93
r 0.10

o P0 16.42
16 42

PE 0    7.69
EPS1 2 1.0675

2010 / Yichuan Liu 12


Example 3: Globex Corporation
 The dividend yield for shares of the Union Pacific
Railroad is 1.9%. Security analysts are forecasting
rapid growth in Globex’s earnings per share (EPS),
about 12.7% per year for the next three years. Does
that imply an expected rate of return of 1.9 + 12.7 =
14.6%?
6%? EExplain.
l i

2010 / Yichuan Liu 13


Example 3: Globex Corporation
 Answer:
No.
o EPS is only growing at 12.7% for the next three years, not

fforever. The
h expectedd rate off return can only
l increase b

by
less than that amount.
o There mayy be a cost to the rappid growth (e.g.
g part of the
current earnings may be retained), so the rate of return is
lowered further.

2010 / Yichuan Liu 14


MIT OpenCourseWare
http://ocw.mit.edu

15.401 Finance Theory I

Fall 2008

For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

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